f(x) = \\begin{cases}-x - 2&\\text{if }x < - 2\\\\\\frac{5}{2}x&\\text{if }x\\geq - 2\\end{cases}\nselect…

f(x) = \\begin{cases}-x - 2&\\text{if }x < - 2\\\\\\frac{5}{2}x&\\text{if }x\\geq - 2\\end{cases}\nselect points on the graph to plot them. select \point fill\ to change a point from closed to open.

f(x) = \\begin{cases}-x - 2&\\text{if }x < - 2\\\\\\frac{5}{2}x&\\text{if }x\\geq - 2\\end{cases}\nselect points on the graph to plot them. select \point fill\ to change a point from closed to open.

Answer

Explanation:

Step1: Analyze (x < - 2) part

For (y=-x - 2) when (x=-3), (y=-(-3)-2=1). So we have the point ((-3,1)). When (x = - 2), for (y=-x - 2), (y=-(-2)-2 = 0), but since (x < - 2), the point ((-2,0)) is open.

Step2: Analyze (x\geq - 2) part

For (y = \frac{5}{2}x), when (x=-2), (y=\frac{5}{2}\times(-2)=-5), and this point ((-2,-5)) is closed. When (x = 0), (y=\frac{5}{2}\times0 = 0), so we have the point ((0,0)). When (x = 2), (y=\frac{5}{2}\times2=5), we have the point ((2,5)).

Answer:

Points to plot: Open point at ((-2,0)), closed point at ((-2,-5)), ((-3,1)), ((0,0)), ((2,5)) (and other points calculated from the two - part function as needed for a more complete graph)